Globally Convergent Distributed Network Localization Using Locally Measured Bearings

This paper studies the problem of bearing-based network localization, which aims to estimate the absolute positions of the nodes in a network by using the inter-node bearings measured in each node's local reference frame and the absolute positions of a small number of nodes called anchors. In the first part of the paper, we propose a continuous-time localization algorithm, which consists of coupled orientation and position estimation procedures. Compared to the existing works, the proposed algorithm has a concise form and guarantees global estimation convergence. In the second part of the paper, we study the discrete-time case which is still an open problem till now. We fill this gap by proposing a discrete-time localization algorithm to globally localize three-dimensional networks using locally measured bearings. The discrete-time algorithm does not require designing sufficiently small step sizes to ensure convergence. Numerical simulation is presented to verify the proposed algorithms.